Open AccessPontryagin maximum principle for the optimal control of linearized compressible navier-stokes equations with state constraints
Author(s) -
Stefan Doboszczak,
Manil T. Mohan,
S. S. Sritharan
Publication year - 2022
Publication title -
evolution equations and control theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 19
eISSN - 2163-2480
pISSN - 2163-2472
DOI - 10.3934/eect.2020110
Subject(s) - mathematics , maximum principle , bounded function , variational principle , semigroup , mathematical analysis , optimal control , type (biology) , pontryagin's minimum principle , compressibility , state (computer science) , domain (mathematical analysis) , partial differential equation , mathematical optimization , physics , ecology , algorithm , biology , thermodynamics
A Pontryagin maximum principle for an optimal control problem in three dimensional linearized compressible viscous flows subject to state constraints is established using the Ekeland variational principle. Since the system considered here is of coupled parabolic-hyperbolic type, the well developed control theory literature using abstract semigroup approach to linear and semilinear partial differential equations does not seem to contain problems of the type studied in this paper. The controls are distributed over a bounded domain, while the state variables are subject to a set of constraints and governed by the compressible Navier-Stokes equations linearized around a suitably regular base state. The maximum principle is of integral-type and obtained for minimizers of a tracking-type integral cost functional.